A Picture on a Line

A range of numbers is easiest to see on a number line. x > 2 is every number to the right of 2, so the picture is an arrow starting at 2 and running right forever. The dot at 2 is left open (hollow), because 2 itself is not a solution: 2 is not greater than 2.

x > 2: an open dot at 2, shaded to the right

x < -1 points the other way: an open dot at -1 and shading to the left, because the solutions are the numbers smaller than -1.

x < -1: an open dot at -1, shaded to the left

The direction of the sign and the direction of the shading agree: the arrow of the inequality points where the shading goes.